... there are good reasons to believe that nonstandard analysis, in some version or other, will be the analysis of the future. Kurt Gödel [1973]

Had a late night last night reading some more on nonstandard analysis, aka deriving calculus from infinitesimals (like Leibniz always intended), instead of from epsilon-delta limits.

My first taste was from the aforementionedWhere Mathematics Comes From some months back, so I already knew pretty much what was going on at an intuitive level--now I was wanting some more rigorous meat to flesh it out. (BTW, it was so thought-provoking that, between that and inertia/laziness, I'm probably going to keep it after all.)

I dug these pages up via Google a number of weeks ago but didn't give them more than a passing glance. First I looked at this page and its subpages. The subpage How to make infinitesimals taxed my math minor to its limit (no pun intended).

Actually, it taxed it beyond its limit: I then figured out that I was missing some crucial bit of information by not knowing what it meant when it casually said that the function m() was a measure. So I dug around on Mathworld a while, learning about sigma algebras (and wondering how the completion of a measure by adding subsets of measure zero can be claimed to be another sigma algebra, since there's no evident guarantee that the complements of these newly-added sets are also being added [by virtue of also having measure zero], which is required by its definition) and superstructures, and browsing various related entries in the process. Somewhere in there I also looked at their own nonstandard analysis page.

Armed with that new knowledge and my still-thoroughly-taxed math minor, I went back to the original page and slogged my way through each step, understanding pretty much everything as I went.

Not satiated, I then sailed over to Another View of Nonstandard Analysis for more. It promised to take an easier, more relaxed approach that wouldn't tax my math minor so hard. It was easier to follow, but that may have been because of my (now extensive) prior exposure to the concepts--which was good, so that I didn't have to feel like several hours' worth of reading went down the drain... I managed to prove all the theorems stated as "consequences" of the axioms, except for the ultrafilter one. Though the one about sequences of zeroes and ones mapping to zero or to one took me until my shower this morning to finally see through (hint for those of you trying this at home: In classic Inventor's Paradox fashion, it's easier to prove a stronger result pertaining to such a bit vector and its complement).

One thing it omitted from the axioms in section 2 is the definition of less-than, which I had to borrow from the first section (I managed to prove that that definition is equivalent to the definition used in the first writeup).

Sleep drove me away from the screen before I could fully digest the last section, on transfer principles. I might yet take a crack at it before I log off for the night...

Yikes, been a while. I drifted from the scene for a while there... Got too many other interesting things going on that distract me (is this what's known colloquially as "a life"? ;) ).

As far as Free Software, most of my time is spent either hanging out in IRC (to the extent that counts as a contribution to the cause) or, typically more productively, checking packages for the Debian IPv6 Project. I always go for the packages that either obviously have no network component, or that are likely to not be IPv6-compliant and are likely easy to prove such. I'm not qualified to proclaim something compliant, but it's a lot easier to pick through things like the CPAN module that lets you write Perl programs in Latin, and proclaim them entirely networking-free.

Inundated with interesting diary entries and other pieces to read. Must try to respond briefly to them...

Came across thesetwo pieces from vmyths.com tonight. Wow. The essential, slightly-exaggerated thesis is that most of the modern-day antivirus software industry is a sham. A must-read.

bgeiger: Funny, I saw a Go set at Barnes and Noble (brick & mortar edition) a few weeks ago, in the Games section. I'm quite sure it was less than $30, too.

palsky: Hey, if people don't like 'em, they'll just rate your diary down so they don't have to read 'em. From where I stand, at the moment your diary's rated 7.7, which is pretty good, so I wouldn't be concerned. What you have to say looks pretty topical to me.

Maybe smaller chunks more frequently would help, though. Maybe you could have split the version control commentary off to another diary entry a few days later, for example.

Mom got me a Roomba for Christmas. It was backordered for a long time, so it didn't come until the second half of January. I've been running it on occasion for a couple of weeks now.

By and large, it works as advertised. The first thing I noticed about it is that it drains its battery rather quickly. It takes up to 14 hours to charge the battery (they claim 12 but it's definitely longer for me), at most 2.5 to completely use it up. I can't cover my whole apartment on one charge.

I don't especially want to run it at night after work (nobody lives below me right now but I don't want to disturb the neighbors on the sides with thudding on the walls), and I'm still not at the point when I can just start it and leave for work--need to get the pattern down of what to put away and what I can safely leave out. So that means I can only run it on the weekends. That gives me plenty of time to charge the battery, but if I'm trying to get things clean, it's difficult. Then again, vacuuming 2/3 the apartment once a week is better than... well, we won't go there.

I found that I was filling the dust bin completely full after each run. Last week I just ran it in my living room area about three times (one charge's worth). The first two times it filled up. After the second time I finally decided to act upon the wise advice the manual provides, that Roomba is great for light work but it doesn't replace the occasional (ahem--like I said, we won't go there) deep cleaning from ye olde upright. So I got it out and went over the same area again. After the third Roomba run the dust bin wasn't full--it was less than 1/3 filled. I guess the rest of the apartment needs that same treatment.

So one of the educational things for me in this is getting to see exactly how much dirt was being picked up from the carpet after each run. With a traditional vacuum with a bag it all goes together so you just see how much you've accumulated over time, not how much you pulled out that day (and thus how much accessible dirt must have accumulated since your last run, leaving you to wonder just how much is buried down deep...).

One other minor nuisance: Twice on Saturday it decided that it was finished for its run while it was right underneath the metal shelves I use for my TV stand. I had to reach under and drag it out. I'm glad that so far it hasn't decided to call it quits while in the corner underneath my bed... I'd really like to see a "seek to home" feature where it runs around for a while, then heads back to the charging station to charge up for a while (14 hours in my case, 2 if I got the deep charger). That becomes a problem right away if the charging station is in another room, but obviously you closed all the doors or put infrared walls up to keep it in this one... which quickly gets us out of the area where low cost and high tech intersect.

I used to have caffeine as a regular part of my life, but for several years now I've cut way back. I used to be able to hang out with the guys and we each drink our own 2-liter of Faygo, frequently Moon Mist (their knockoff of Mountain Dew). We'd stay up all night doing our thing (whatever thing it was that night). I didn't sweat it.

I don't attribute this to getting older, just to getting wiser. At some point I started realizing that I didn't always want to be under its influence, so I started indulging in the lower-caffeine alternatives instead of the colas or the fluorescent-yellow precipitationally-named sodas (though since I'm talking about my Michigan years I guess I should say "pop" ;) ). Now I don't drink caffeine unless it's because I need a specific boost, or if it's with the old crew in Detroit on occasion (I guess that makes me a "social caffeine drinker")--but the last time I did that to a significant degree (some year ago), I really felt it. Again, I don't call it getting older--I'm sure I can handle it as well as I ever did--it's just that now I'm not as acclimated to getting that frequent dose, so I noticed it way more, and I decided I didn't like it. I've heard that using caffeine continually means it doesn't give you the boost it would if you used it sparingly, so that's another reason to lay off of it.

Then over the years (especially since I moved out here) a similar thing has happened where sugar is concerned. So now I don't drink soda much at all any more. Mostly it's milk or water, with Powerade at home for an occasional changeup, or sometimes juice. But I'm not knocking down two- (or three!) liter bottles any longer--and certainly not at one sitting.

The biggest exception is Vernors, which I've started finding outlets for around the Metroplex. It's amazing: I almost never drank it when I was growing up there. I think I went 5-10 years with nary a sip. (Much of that probably was that no fast food restaurants that I can think of ever served it.) It's just something we took for granted. Then I moved away from Michigan for several years, and somewhere in there I took a liking to Canada Dry's ginger ale, but once I tried some just Vernors for old times' sake, I decided I missed it! I've spoken to other expat Midwesterners about this and every one has spoken fondly of it and said they missed it. Then I get to spring it on them that they can get it around DFW now. In one case I bought two 2-liters for a couple as a surprise Christmas gift. They were ecstatic... and my Mom who was visiting from Detroit watched the whole scene and said, "I don't believe this!" It was hysterical for me because I've been on both sides: missing it and unable to get it, and taking it for granted and forgetting about it.

Boy, that was a nice ramble... So I occasionally wind up with a 2-liter of Vernors in the fridge, and unlike most other sodas that might find their way in there, it usually doesn't go flat before it's gone nor sit there for a long time unopened. Other than that, soda seldom makes its way into my system.

I never could get into coffee, so soda is my only source of caffeine. (Penguin Mints just don't have that same appeal.) Mom was addicted to Starbucks for a while--she got to the point where she started getting shakes when she drank it, so she quit. It was hard on her but she didn't think she had much of a choice.

mharris: Definitely good stuff here. So good, in fact, that it's a shame that it and its replies weren't in an Advogato article instead. It's much less likely to get lost in the noise over time if it's an article, and will probably draw more responses--certainly more readers!

Speaking of which, I wrote an article about the Advogato trust metric last week, which I'll be editing and posting soon--perhaps today.

Interestingdiscussion recently about wavelets. As it happens, I picked up The World According to Wavelets as an impulse buy right after Christmas. It's technically in my pile of "I'll get around to looking at this one of these years" books, but with the spate of links here, it looks like I'll be reading up on wavelets sometime soon after all. (Or not. <sigh>)

Sheesh, I leave you people alone for a few days, and what happens?... :)

chromatic: This was on my list of things to write about on here, so I guess I'll give it a brief treatment here.

Close to two years ago I went to a training class at
work called "Consulting Skills". Almost the first thing they taught us was personality types. The
methodology
they used had four quadrants. On the y-axis they labelled the top as "dominant" and the bottom as "submissive". On the x-axis they labelled the right as "task-oriented" and the left as "people-oriented".

Computer nerds such as ourselves usually fall in the lower right quadrant. We're more task-oriented than people-oriented, so things, and in particular accomplishments, appeal to us more than interacting with people, as a general rule. So meeting random people at a party would be draining to us, but would be enjoyable or even stimulating to people on the left side.

Similarly, we're more on the submissive side. The type in the upper right is also task-oriented, but they're more of the take-charge types. (They're more likely to be project managers, for example.) They'd rather make a snap decision and deal with the consequences than analyze and agonize. If a job needs to be done, they'd just jump in and start doing it, and try to fix the mess they created later, whereas our type would say, "Whoa, wait a minute, let me stop and think about this/do some research/review the existing codebase/read a few O'Reilly books on the subject first."

We're more attentive to the details. If there's a typo in a document or a program we're the first to notice it. (I have an award certificate hanging on my wall, from my volunteer service at my church. The first thing I noticed when I got it was that they had two spaces between a pair of words when they had the expected one space between words everywhere else. It just jumped out at me--that's the first thing my eye landed on. I figured it would be ungrateful to complain about it, so I didn't say anything, and over the past year that I've had it I've learned to not let it bug me.)

I wanted to learn more on the subject, but I didn't have anything meaningful to search on, since searches such as "personality type" would come up with things like Meyer-Briggs. MBTI is nice and all, but it's not a "pocket methodology": You can't easily apply it to somebody when you're in a conversation with them, whereas with this methodology you can see which quadrant(s!) people live in rather easily, so you can gain useful information about them, and about how to relate to them, without asking them to fill out a 100-question survey first.

Eventually I started stumbling upon some books that talk about this. Various sources recognize the four personality types, but most of them categorize them descriptively--only a few (the author of our instructor's materials being one of them) arrange them into quadrants, which is what makes it even more useful.

But apparently people started classifying people into these four types way back in ancient Greek times. A Greek philosopher (don't ask me to remember who right now) coined some labels for the types, which he termed "humours", which many people have used over the years. (That's what finally enabled me to do useful net searches.)

He used the labels choleric, sanguine, phlegmatic, and melancholy.

Guess which label is used for the lower-right quadrant?

I read somewhere once a commentary on how surprising it was that computer science was adopted as an academic discipline as rapidly as it was. It seemed like it didn't take very long (within two decades perhaps?) for computer science departments, distinct from mathematics and physics/electrical engineering, to spring up at universities worldwide. (I guess the assertion is that other areas, such as other hard sciences, soft sciences like psychology, or fine/liberal arts, took much longer, centuries even, to be honored with such recognition.) The author speculated that computer science appealed to something in certain personality types that nothing else in history adequately tapped into, so when computer science per se came into being, people who were unfulfilled in other disciplines flocked to it.

So I'd definitely go with your hypothesis that it's something about the field that draws certain people with certain attributes, rather than something about the field that instills certain attributes into people.

You said:

[S]ometimes I care a great deal about what kind of a world I'm helping to build. I want to make a place of peace, a place of learning, a place of healing, and a place that helps people to become better and more complete. It's a huge goal, and the best way I know of is to be a good example.

For me, that's my church. But I think I take your point, that we have to think about things bigger than just technology and what's cool today. (RMS's point is the same, but from a different angle.) And of course my church encourages being a good example...

BTW, looks like Advogato's diary-posting mechanism is either going up and down or is extremely slow; hoping I can actually get all this text posted.